(RLC circuit) The circuit in the figure consists of a resistor (R ohms), an inductor (L henrys), a capacitor (C farads), and an initial voltage source. Let h = R/(2L), and suppose R, L, and C have been selected so that b also equals 1//LC. (This is done, for instance, when the circuit is used in a voltmeter.) Let v(t) be the voltage (in volts) at time t, measured across the capacitor. It can be shown that v is in the null space H of the linear transformation that maps v(t) into Lv"(t) + Rv'(t) + (1/C)v(t), and H consists of all functions of the form v(t) = e¬b' (c1 + c2t). Find a basis for H. Voltage source

(RLC circuit) The circuit in the figure consists of a resistor (R ohms), an inductor (L henrys), a capacitor (C farads), and an initial voltage source. Let h = R/(2L), and suppose R, L, and C have been selected so that b also equals 1//LC. (This is done, for instance, when the circuit is used in a voltmeter.) Let v(t) be the voltage (in volts) at time t, measured across the capacitor. It can be shown that v is in the null space H of the linear transformation that maps v(t) into Lv"(t) + Rv'(t) + (1/C)v(t), and H consists of all functions of the form v(t) = e¬b' (c1 + c2t). Find a basis for H. Voltage source

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 67E

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